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    First of all, I completely agree with bb193's statement - you need to be equally proficient with solving quadratics by factorising, CTS and the quadratic equation.

    (Original post by Conal09)
    Can you just confirm this for me? So you have -2 1/2 and then, to get -5, you multiply through by 2? And in doing so you get 2(x-1)^2? That's where I went wrong in that method
    Sorry, couldn't reply earlier because I lost track of time and have to run (ice-skate?) to the bus stop to get into town!

    Sorry if this explanation becomes patronising at any point, it isn't meant to be.

    When you expand the brackets (a+b)^2, you get a^2 + 2ab + b^2.

    What I've done is rewrite (x^2 - 2x) into a set of squared brackets. Hence the (x-1)^2. These two forms aren't actually equal - if you multiply out (x-1)^2 you'll have an extra +1 because of the (-1)*(-1) term. To make (x^2 - 2x) into (x-1)^2, we need to subtract 1 as well.

    Hence, the (-1 - (3/2)). This multiplied by 2 gives (-2 - 3) = -5.


    EDIT: I think that was possibly the least clear explanation I've ever given. PM if it still doesn't make sense.
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    (Original post by Conal09)
    Can you just confirm this for me? So you have -2 1/2 and then, to get -5, you multiply through by 2? And in doing so you get 2(x-1)^2? That's where I went wrong in that method
    Pretty much.

    2[(x-1)^2-1-\frac{3}{2}] = 0

    What we want to do is multiply out the brackets so we can simplify it all. The 2 on the outside makes it really annoying to solve for x, because x is inside. To get rid of the 2 we can multiply everything inside the square brackets by 2. Do each bit one by one:

    (x-1)² multiplied by 2 is 2(x-1)².
    -1 multiplied by 2 is -2
    -3/2 multiplied by 2 is -3

    So what we have is:

    2(x-1)²-2-3=0 which is the same as writing 2(x-1)²-5=0

    You can then solve for x.

    -------

    Another way of doing it is straight away dividing both sides of 2[(x-1)^2-1-\frac{3}{2}] = 0 by 2, because all we want to do is get rid of the big 2 on the outside and this would do the trick nice and quickly.

    If we pretend z=[(x-1)^2-1-\frac{3}{2}] you can see that the original equation could be written as 2z=0.

    Dividing 2z by 2 would give you z, and dividing 0 by 2 would give you 0.
    So what you're left with is:

    z=0;

    (x-1)^2-1-\frac{3}{2}=0

    Remember that 1 could be rewritten as \frac{2}{2}; -\frac{2}{2}-\frac{3}{2} = -\frac{5}{2}

    Grouping all the numbers together on one side, and the x on the other side, you end up with:

    (x-1)^2=\frac{5}{2}
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    Btw: \sqrt\frac{5}2 is the same as root 5 over root 2. You get root 10 over 2 by multiplying top and bottom by root 2.
 
 
 
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